Random magnetism in the frustrated triangular spin ladder $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$

We present susceptibility, high-field magnetization, and Raman scattering measurements of the frustrated spin system $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$, consisting of ladders of ${\mathrm{Cu}}^{2+}$ tetrahedra. The magnetic susceptibility shows a sub-Curie power-law behavior $\chi \left(T\right)\sim T^{-{\alpha }_s}$ with ${\alpha }_s=0.43$ and 0.60 for low temperatures $8\mathrm{K}<T<20\mathrm{K}$ and intermediate temperatures $20\mathrm{K}<T<140\mathrm{K}$, respectively. The magnetization at $8\mathrm{K}$ also follows a power law $M\propto H^{1-{\alpha }_m}$ with ${\alpha }_m=0.45$, indicating that the magnetic behavior is dominated by random interactions. Raman scattering measurements show substantial local lattice distortions arising from a change of covalency as a function of temperature. Our study suggests that a random spin singlet state can be realized in low-dimensional frustrated spin systems induced by temperature-dependent lattice distortions.

Figure 1

(a) and (b) Perspective sketch of the spin topology of $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$. The numbers on the solid circles denote the crystallographically inequivalent Cu-sites. (c) Static susceptibility of $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$ as a function of temperature. The open circle is the raw data and the solid line is a fit using a sum of a temperature-independent contribution (the dotted-dashed line), a Curie-Weiss law (the dashed line), and a noninteracting dimer term (the dotted-dotted-dashed line). The inset shows a power-law behavior with a change of the exponent at around $500\mathrm{K}$ in the log-log plot.

Figure 2

Magnetization as a function of magnetic field for $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$ at $8\mathrm{K}$ and $20\mathrm{K}$, respectively. The inset shows the power-law behavior of the magnetization $M\left(H\right)\propto H^{1-{\alpha }_m}$ with ${\alpha }_m=0.45$ for sufficiently high magnetic fields $20\mathrm{T}<H<50\mathrm{T}$ at $8\mathrm{K}$ on a log-log plot.

Figure 3

(Upper panel) Comparison of Raman spectra of $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$ at $5\mathrm{K}$ and $600\mathrm{K}$ in (aa) polarization. (Lower panel) Temperature dependence of frequency of the $213{\mathrm{cm}}^{-1}$ and $958{\mathrm{cm}}^{-1}$ phonon modes. The respective mode is indicated by the vertical arrows in the upper panel.

Figure 4

(a) Raman spectra of $\mathrm{K}{\mathrm{Cu}}_5{\mathrm{V}}_3{\mathrm{O}}_{13}$ in the high-temperature and low-frequency regime. The inset shows a fit of a collision-dominated model to Raman spectra at $500\mathrm{K}$. (b) Temperature dependence of phonon modes in the high frequency regime. The inset shows the temperature dependence of integrated intensity of the $958{\mathrm{cm}}^{-1}$ mode. The line is a guide to the eye.

Figure 5

(a) Spin configuration at a specific temperature $T_1$: the number denotes crystallographically different Cu-sites with spin $S_i=1∕2$ $(i=1-5)$. The solid lines between $i$ and $j$ ${\mathrm{Cu}}^{2+}$ ions represent exchange paths and coupling constants $J_{ij}$. The dashed ellipsoids denote exchange-coupled singlet pairs. Quasi-free ${\mathrm{Cu}}^{2+}$ ions that are only weakly coupled to the neighbors are depicted using arrows. (b) Spin configuration at a different temperature $T_2$.